Representing Finite Groups: A Semisimple Introduction

✍ Scribed by Ambar N. Sengupta (auth.)

Publisher: Springer-Verlag New York
Year: 2012
Tongue: English
Leaves: 382
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material.

Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful.

A separate solutions manual is available for instructors.

✦ Table of Contents

Front Matter....Pages i-xv
Concepts and Constructs....Pages 1-38
Basic Examples....Pages 39-58
The Group Algebra....Pages 59-81
More Group Algebra....Pages 83-123
Simply Semisimple....Pages 125-156
Representations of S n ....Pages 157-188
Characters....Pages 189-234
Induced Representations....Pages 235-248
Commutant Duality....Pages 249-266
Character Duality....Pages 267-279
Representations of U ( N )....Pages 281-300
Postscript: Algebra....Pages 301-351
Back Matter....Pages 353-371

✦ Subjects

Group Theory and Generalizations;Quantum Physics;Applications of Mathematics;Theoretical, Mathematical and Computational Physics

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